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Properties

Label 6.8
Level 6
Weight 8
Dimension 1
Nonzero newspaces 1
Newform subspaces 1
Sturm bound 16
Trace bound 0

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Defining parameters

Level: N N = 6=2⋅3 6 = 2 \cdot 3
Weight: k k = 8 8
Nonzero newspaces: 1 1
Newform subspaces: 1 1
Sturm bound: 1616
Trace bound: 00

Dimensions

The following table gives the dimensions of various subspaces of M8(Γ1(6))M_{8}(\Gamma_1(6)).

Total New Old
Modular forms 9 1 8
Cusp forms 5 1 4
Eisenstein series 4 0 4

Trace form

q+8q2+27q3+64q4−114q5+216q6−1576q7+512q8+729q9−912q10+7332q11+1728q12−3802q13−12608q14−3078q15+4096q16−6606q17+⋯+5345028q99+O(q100) q + 8 q^{2} + 27 q^{3} + 64 q^{4} - 114 q^{5} + 216 q^{6} - 1576 q^{7} + 512 q^{8} + 729 q^{9} - 912 q^{10} + 7332 q^{11} + 1728 q^{12} - 3802 q^{13} - 12608 q^{14} - 3078 q^{15} + 4096 q^{16} - 6606 q^{17}+ \cdots + 5345028 q^{99}+O(q^{100}) Copy content Toggle raw display

Decomposition of S8new(Γ1(6))S_{8}^{\mathrm{new}}(\Gamma_1(6))

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space Sknew(N,χ) S_k^{\mathrm{new}}(N, \chi) we list available newforms together with their dimension.

Label χ\chi Newforms Dimension χ\chi degree
6.8.a χ6(1,⋅)\chi_{6}(1, \cdot) 6.8.a.a 1 1

Decomposition of S8old(Γ1(6))S_{8}^{\mathrm{old}}(\Gamma_1(6)) into lower level spaces

S8old(Γ1(6))≅ S_{8}^{\mathrm{old}}(\Gamma_1(6)) \cong S8new(Γ1(1))S_{8}^{\mathrm{new}}(\Gamma_1(1))⊕4^{\oplus 4}⊕\oplusS8new(Γ1(2))S_{8}^{\mathrm{new}}(\Gamma_1(2))⊕2^{\oplus 2}⊕\oplusS8new(Γ1(3))S_{8}^{\mathrm{new}}(\Gamma_1(3))⊕2^{\oplus 2}